You mean ~~ancestors~~ *descendants. Also, rest assured! That's not a fear to have: https://www.anl.gov/article/10-myths-about-nuclear-energy

Myth # 5: There is no solution for huge amounts of nuclear waste being generated.

Truth: All of the used nuclear fuel generated in every nuclear plant in the past 50 years would fill a football field to a depth of less than 10 yards, and 96 % of this ​“waste” can be recycled [5]. Used fuel is currently being safely stored. The U.S. National Academy of Sciences and the equivalent scientific advisory panels in every major country support geological disposal of such wastes as the preferred safe method for their ultimate disposal[6].